Problem: Express your answer as a mixed number simplified to lowest terms. $12\dfrac{2}{5}-8\dfrac{2}{3} = {?}$
Explanation: Find a common denominator for the fractions: $= {12\dfrac{6}{15}}-{8\dfrac{10}{15}}$ Convert ${12\dfrac{6}{15}}$ to ${11 + \dfrac{15}{15} + \dfrac{6}{15}}$ So the problem becomes: ${11\dfrac{21}{15}}-{8\dfrac{10}{15}}$ Separate the whole numbers from the fractional parts: $= {11} + {\dfrac{21}{15}} - {8} - {\dfrac{10}{15}}$ Bring the whole numbers together and the fractions together: $= {11} - {8} + {\dfrac{21}{15}} - {\dfrac{10}{15}}$ Subtract the whole numbers: $=3 + {\dfrac{21}{15}} - {\dfrac{10}{15}}$ Subtract the fractions: $= 3+\dfrac{11}{15}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{11}{15}$